A single LC filter section can be used to extend the bandwidth of the baseband output and the chip's baseband equivalent circuit with baseband bandwidth extension is shown in fig 1. With 200O loading, the -0.5dB bandwidth can be extended from 250MHz to 630MHz using a series inductance of 18nH and a shunt capacitance of 4.7pF. In a direct conversion receiver, the second order intermodulation distortion products (IM2) fall directly in band at the baseband frequencies. Take, for example, two equal power rf signals – f1 and f2 – at 2140MHz and 2141MHz, while the LO is 10MHz away at 2130MHz. The resultant IM2 spur would fall at f2 – f1, or 1MHz. The LTC5585 can adjust for minimum IM2 spurs independently on the I and Q channels by using external control voltages (see fig 2 for a typical set up). The differential baseband outputs are combined using a balun and the 1MHz IM2 difference frequency component is selected with a lowpass filter to prevent the strong main tones at 10MHz and 11MHz from compressing the spectrum analyser front end. Without the lowpass filter, 20 to 30dB of attenuation and long averaged measurement times are necessary for good measurement.

**Two calibration strategies**With this optimisation capability, two calibration strategies may be considered. One is a 'set and forget' step at the factory, where a simple trim potentiometer for each adjustment pin suffices. Alternatively, an automatic closed loop calibration algorithm can be implemented in software, allowing the equipment to be calibrated periodically. For DPD receivers that already monitor their transmitters' output, this is trivial; the transmitters can generate the two test tones. For main receivers, this calibration may involve additional hardware to loop back the two test tones to the receiver channel. A similar adjustment capability is integrated into the chip to zero the I and Q's dc output voltage. DC offset, a product arising from internal mismatch and self mixing of the LO and rf input leakages, can diminish the a/d converter's dynamic range when the signal chain is dc coupled throughout. An output dc offset voltage of 10mV, when passed through a 20dB gain stage, would result in 100mV of dc offset at a/d converter's input. With the 2Vp-p input range of a 12bit converter, this effectively reduces the converter's dynamic range by 0.9dB. Potential cost savings make a zero IF receiver particularly compelling, but because zero IF demodulation produces no image at the baseband, there is no need for a relatively expensive SAW filter. Perhaps most attractive of all, the a/d converter's sampling rate can be reduced significantly.

**Theory of operation of I/Q demodulation**The operation of an IQ demodulator can be explained by representing its rf input signal, srf (t), as a combination of two double sideband modulated quadrature carriers. In fig A, the in phase component, I(t), and quadrature component, Q(t), are baseband signals that can be viewed as inputs to an ideal IQ modulator generating srf(t). An IQ demodulator achieves perfect reconstruction of I(t) and Q(t) by exploiting the quadrature phase relation between si(t) and sq(t). The frequency domain representation of a -90° phase shift corresponds to multiplication by the Hilbert transform; H(j?) = -jsgn(?) This converts a spectrum with even symmetry around ?=0 to a spectrum with odd symmetry, and vice versa. The spectra of si(t) and sq(t) therefore exhibit different symmetry; si(t) is even, sq(t) is odd. Down conversion of the even rf input component with the even LO (cosine) retrieves I(t), while sq(t) with the odd LO (sine) retrieves Q(t). Cross combinations of even and odd yield zero. An error, f, on the quadrature relation between the LO outputs causes crosstalk between the I and Q channels. Using the I phase channel as reference, an even component is introduced in the Q channel LO, resulting in a contribution of I(t) to the Q channel output, Qout(t). Another IQ demodulator application is an image rejection/cancellation receiver with non zero IF frequency. Here, the I channel preserves the symmetry in the rf input signal, while the Q channel converts even components to odd and vice versa. The extra 90° phase shifter restores the original symmetry in the Q channel, but with opposite sign for the signals s1(t) and s2(t); the phase of s2(t) is ahead of the LO since its centre frequency is higher, while the phase of s1(t) lags. Addition to the I channel reconstructs the down converted signal s2(t); subtraction reconstructs s1(t). The image rejection is degraded in the presence of a quadrature phase error f or gain mismatch a between I and Q channels. Phase error introduces crosstalk between the channels, while gain mismatch results in imperfect cancellation by the adder.

**Michael Kouwenhoven, design manager, John Myers, design engineer, James Wong, high frequency product marketing manager and Vladimir Dvorkin, applications engineering maqnager, are with Linear Technology.**